Sound Velocities at High Pressure and Temperature and Their Geophysical Implications

Abstract

Temperature coefficients of compressional and bulk sound velocities at pressures on the order of 100 GPa are obtained from Hugoniot sound velocity measurements for solid Al, W, Cu, Ta, and Mg_2SiO_4. The Hugoniot velocities are compared to third-order finite strain extrapolations of velocities along the principal isentrope using ultrasonically determined coefficients. At low pressure, where thermal effects are minor, good agreement is found between the Hugoniot velocities and finite strain extrapolations. At high pressures, differences in velocities and temperatures are used to constrain temperature coefficients of velocity. For all materials studied except W, the temperature coefficients of velocity at pressures above 1 Mbar are a factor of 2 to 8 smaller in magnitude than zero-pressure values. In shock-melted materials, the Hugoniot sound velocities are close to finite strain velocities calculated from low-pressure properties of the solid phase for Mo, Ta, Pb, Fe, and alkali halides. The temperature coefficient determined for the high-pressure phases of forsterite above 100 GPa (| (∂V_P/∂T)_P| = 0.1 ± 0.1 m/s/K) is in agreement with estimates based on elastic and thermodynamic properties for the Earth. Our results indicate that |(∂VP/∂T)_P| is a decreasing function of pressure in contrast to residual sphere studies which suggest |(∂V_P/∂T)_P| is nearly constant with depth in the Earth. In combination with mineral physics estimates of thermal expansivity at High pressure, it is estimated that (∂V_P/∂ρ)_P = 2 (km/s)/(g/cm^3) for P > 100 GPa, with acceptable values ranging from 0 to 8. This overlaps the range of estimated lower mantle values based on seismic and geodetic data. Tomographic and free oscillation data require large increases in the parameter ν = (∂ ln V_S/∂ ln VP)_P under lower mantle conditions, relative to laboratory values. Available data for tungsten and aluminum yield ν values along the Hugoniot that are consistent with zero-pressure values for these materials, although uncertainties are ± 50%. Temperature coefficients of velocity at high pressure are used to make improved estimates of the magnitude of thermal heterogeneities sampled by seismic tomography. Long-wavelength compressional velocity anomalies at pressures in the 100–127 GPa range (2271–2891 km depth) in the lower mantle correspond to temperature variations of 120 ± 100 K, whereas those in the D″ region are likely to be a factor of 3 to 4 larger.

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